Question

6.2b (l)

1. which set of numbers correctly shows a number, its opposite, and its absolute value,

in that order?
a 16.3 -16.3 -16.3
b 42.5 -42.5 42.5
c 30.8 30.8 -30.8
d -97.1 97.1 -97.1

6.2d (l)

1. which decimal is greater than 0.5 but less than 0.99?

a 0.25
b 0.5
c 0.8
d 0.998

6.7a (l)

1. in the following expression, which calculation should be performed first?

2 × 4 - 3 + (2 - 1)
a 2 × 4
b 4 - 3
c 3 + 2
d (2 - 1)

Explanation:

Question 1

To determine the correct set, we recall: The opposite of a number \( a \) is \( -a \), and the absolute value \( |a| \) is \( a \) if \( a \geq 0 \), \( -a \) if \( a < 0 \).

• Option A: Absolute value of \( 16.3 \) is \( 16.3 \), not \( -16.3 \). Incorrect.
• Option B: Opposite of \( 42.5 \) is \( -42.5 \), absolute value is \( 42.5 \). Correct.
• Option C: Opposite of \( 30.8 \) is \( -30.8 \), not \( 30.8 \). Incorrect.
• Option D: Absolute value of \( -97.1 \) is \( 97.1 \), not \( -97.1 \). Incorrect.

We check which decimal satisfies \( 0.5 < x < 0.99 \).

• Option A: \( 0.25 < 0.5 \). Incorrect.
• Option B: \( 0.5 \) is not greater than \( 0.5 \). Incorrect.
• Option C: \( 0.5 < 0.8 < 0.99 \). Correct.
• Option D: \( 0.998 > 0.99 \). Incorrect.

By the order of operations (PEMDAS/BODMAS), parentheses are evaluated first. In \( 2 \times 4 - 3 + (2 - 1) \), the parentheses \( (2 - 1) \) must be calculated first.

Answer:

B. 42.5 -42.5 42.5

Question 2